Related papers: Resonances in Loewner equations
In [5], O. Bauer interpreted the chordal Loewner equation in terms of non-commutative probability theory. We follow this perspective and identify the chordal Loewner equations as the non-autonomous versions of evolution equations for…
In this note we unify the results of A.C. Lazer and P.O. Frederickson [3], A.C. Lazer [6], A.C. Lazer and D.E. Leach [7], J.M. Alonso and R. Ortega [1], and P. Korman and Y. Li [4] on periodic oscillations and unbounded solutions of…
In this paper, we study the following problem $$ \{{ll} \Delta_{H^n} u-u+u^p=0 & in H^n u>0& in H^n u(x)\to 0 &\rho(x)\to\infty}. $$ where $1<p < \frac{Q+2}{Q-2}$, Q is the homogeneous dimension of Heisenberg group $H^n$. Our main result is…
In this paper we adapt the method of [P. H. Baptistelli, M. Manoel and I. O. Zeli. Normal form theory for reversible equivariant vector fields. Bull. Braz. Math. Soc., New Series 47 (2016), no. 3, 935-954] to obtain normal forms of a class…
We study the existence of $T$-periodic solutions $(T > 0)$ for the first order differential equations being at resonance at infinity, where the right hand side is the perturbations of a sectorial operator. Our aim is to prove an index…
In this paper, we consider the Diophantine equation $\lambda_1U_{n_1}+\ldots+\lambda_kU_{n_k}=wp_1^{z_1} \cdots p_s^{z_s},$ where $\{U_n\}_{n\geq 0}$ is a fixed non-degenerate linear recurrence sequence of order greater than or equal to 2;…
The seminal work of DiPerna and Lions [Invent. Math., 98, 1989] guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suitable selection of trajectories of the related ODE satisfying…
We are concerned with periodic problems for nonlinear evolution equations at resonance of the form $\dot u(t) = - A u(t) + F (t,u(t))$, where a densely defined linear operator $A\colon D(A)\to X$ on a Banach space $X$ is such that $-A$…
We show that for every positive integer $k$ there are positive constants $C$ and $c$ such that if $A$ is a subset of $\{1, 2, \dots, n\}$ of size at least $C n^{1/k}$, then, for some $d \leq k-1$, the set of subset sums of $A$ contains a…
We study positive singular solutions of the Loewner-Nirenberg problem on conical domains and establish the existence of solutions that admit prescribed asymptotic expansions near vertices, valid to arbitrarily high order of approximation.
Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers $\{F_n\}$, where we take $F_1=1$ and $F_2=2$. This has been generalized for any Positive Linear…
We prove the existence of a continuous family of positive and generally non-monotone travelling fronts in delayed reaction-diffusion equations $u_t(t,x) = \Delta u(t,x)- u(t,x) + g(u(t-h,x)) (*)$, when $g \in C^2(R_+,R_+)$ has exactly two…
We prove that every subset of $\{1,\dots, N\}$ which does not contain any solutions to the equation $x+y+z=3w$ has at most $\exp(-c(\log N)^{1/5+o(1)})N$ elements, for some $c>0$. This theorem improves upon previous estimates. Additionally,…
We provide a sufficient condition for the existence of a positive solution to $-\Delta u+V(|x|) u=u^p$ in $B_1$, when p is large enough. Here $B_1$ is the unit ball of $R^n$, n greater or equal to 2, and we deal both with Neumann and…
We consider a planar Hamiltonian system of the type $Jz' = \nabla_z H(t,z)$, where $H: \mathbb{R} \times \mathbb{R}^2 \to \mathbb{R}$ is a function periodic in the time variable, such that $\nabla_z H(t,0) \equiv 0$ and $\nabla_z H(t,z)$ is…
In the present paper, we apply a global branch approach to study the existence, non-existence and multiplicity of positive normalized solutions $(\lambda_c, u_c)\in \mathbb{R}\times H^1(\mathbb{R}^N)$ to the following Kirchhoff problem $$…
In this article we prove that nonlinear resolvents of infinitesimal generators on bounded and convex subdomains of $\C^n$ are decreasing Loewner chains. Furthermore, we consider the problem of the existence of nonlinear resolvents on…
A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. We consider a family of nonlinear recurrences with the Laurent property, which were…
In this paper we consider a linear homogeneous system of $m$ equations in $n$ unknowns with integer coefficients over the reals. Assume that the sum of the absolute values of the coefficients of each equation does not exceed $k+1$ for some…
We prove existence of positive ground state solutions to the pseudo-relativistic Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{l} \sqrt{-\Delta +m^2} u +Vu = \left( W * |u|^{\theta} \right)|u|^{\theta -2} u \quad\text{in…